HYPOTHESIS TESTING

  I.  Introduction.
        A.  The role of hypothesis testing in the scientific endeavor. 
        B.  The logic of hypothesis testing. 
              1.  Begin with a hypothesis based on theory or previous 
                  research. 
              2.  Collect empirical data to test the hypothesis.
              3.  Analyze the data to see if hypothesis is correct.
        C.  The relationship between estimation and hypothesis testing. 

 II.  The steps in hypothesis testing. 
        A.  State your null hypothesis. 
              1.  A statitistical test must have something to test or 
                  evaluate.  That something is the null hypothesis.  
                  It is typically a simple mathematical or verbal 
                  statement about population parameters such as "the 
                  two variables are independent" or "the two variables 
                  are equal." 
              2.  The null hypothesis is always stated in the null or 
                  most neutral form.  Typically, this means to state 
                  that two values are equal or that there is no 
                  difference in two values or that there is no 
                  relationship between two variables.
              3.  The null may not be what the researcher actually 
                  hypothesizes to be true.  The researcher may actually 
                  hypothesize that there is a difference or that two 
                  values are not equal.  This alternative hypothesis is 
                  called the research hypothesis.  
              4.  The null is tested because it is easier to evaluate.  
              5.  If the null is rejected it offers support for the 
                  research hypothesis.  
        B.  Determine the best statistical test.
              1.  Each hypothesis test requires that a test statistic 
                  be calculated.  The test statistic calculated 
                  depends on the type of hypothesis being evaluated. 
              2.  Underlying each test statistic is sampling 
                  distribution by which the probability of obtaining 
                  certain test statistics can be evaluated. 
              3.  There are several different sampling distributions.  
                  Thus far we have talked about two:  the z and t 
                  distributions.  Others will be introduced later. 
        C.  Check the basic assumptions. 
              1.  Every test statitistic and sampling distribution is 
                  based on certain assumptions.  Some of the most 
                  common assumptions relate to the nature of the 
                  sample (is it a probability sample), the level of 
                  measurement of the variable being analyzed (is it 
                  nominal, ordinal, or interval), and the shape of 
                  the sampling distribution (is it normal).  However, 
                  there are other assumptions as well. 
              2.  Before performing a statististical test, you must 
                  be certain the assumption on which it is based hold 
                  true. 
        D.  Select an alpha level (significance level).  
              1.  Alpha level, sampling error, and probability. 
              2.  Alpha level as the probability of rejecting a null 
                  hypothesis when it is actually true. 
              3.  One- and two-tailed tests. 
        E.  Calculate the test statistic.
        F.  Determine the probability associated with the test statistic. 
        G.  Compare the obtained probability to the alpha level and make a
	    decison about the null.